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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code>.SpectralEmbedding</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-manifold-spectralembedding">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.SpectralEmbedding</span></code></a></li>
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  <div class="section" id="sklearn-manifold-spectralembedding">
<h1><a class="reference internal" href="../classes.html#module-sklearn.manifold" title="sklearn.manifold"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code></a>.SpectralEmbedding<a class="headerlink" href="#sklearn-manifold-spectralembedding" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.manifold.SpectralEmbedding">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.manifold.</code><code class="sig-name descname">SpectralEmbedding</code><span class="sig-paren">(</span><em class="sig-param">n_components=2</em>, <em class="sig-param">affinity='nearest_neighbors'</em>, <em class="sig-param">gamma=None</em>, <em class="sig-param">random_state=None</em>, <em class="sig-param">eigen_solver=None</em>, <em class="sig-param">n_neighbors=None</em>, <em class="sig-param">n_jobs=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_spectral_embedding.py#L353"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding" title="Permalink to this definition">¶</a></dt>
<dd><p>Spectral embedding for non-linear dimensionality reduction.</p>
<p>Forms an affinity matrix given by the specified function and
applies spectral decomposition to the corresponding graph laplacian.
The resulting transformation is given by the value of the
eigenvectors for each data point.</p>
<p>Note : Laplacian Eigenmaps is the actual algorithm implemented here.</p>
<p>Read more in the <a class="reference internal" href="../manifold.html#spectral-embedding"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>n_components</strong><span class="classifier">integer, default: 2</span></dt><dd><p>The dimension of the projected subspace.</p>
</dd>
<dt><strong>affinity</strong><span class="classifier">string or callable, default</span></dt><dd><dl class="simple">
<dt>How to construct the affinity matrix.</dt><dd><ul class="simple">
<li><p>‘nearest_neighbors’ : construct the affinity matrix by computing a
graph of nearest neighbors.</p></li>
<li><p>‘rbf’ : construct the affinity matrix by computing a radial basis
function (RBF) kernel.</p></li>
<li><p>‘precomputed’ : interpret <code class="docutils literal notranslate"><span class="pre">X</span></code> as a precomputed affinity matrix.</p></li>
<li><p>‘precomputed_nearest_neighbors’ : interpret <code class="docutils literal notranslate"><span class="pre">X</span></code> as a sparse graph
of precomputed nearest neighbors, and constructs the affinity matrix
by selecting the <code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> nearest neighbors.</p></li>
<li><p>callable : use passed in function as affinity
the function takes in data matrix (n_samples, n_features)
and return affinity matrix (n_samples, n_samples).</p></li>
</ul>
</dd>
</dl>
</dd>
<dt><strong>gamma</strong><span class="classifier">float, optional, default</span></dt><dd><p>Kernel coefficient for rbf kernel.</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, optional, default: None</span></dt><dd><p>A pseudo random number generator used for the initialization of the
lobpcg eigenvectors.  If int, random_state is the seed used by the
random number generator; If RandomState instance, random_state is the
random number generator; If None, the random number generator is the
RandomState instance used by <code class="docutils literal notranslate"><span class="pre">np.random</span></code>. Used when <code class="docutils literal notranslate"><span class="pre">solver</span></code> ==
‘amg’.</p>
</dd>
<dt><strong>eigen_solver</strong><span class="classifier">{None, ‘arpack’, ‘lobpcg’, or ‘amg’}</span></dt><dd><p>The eigenvalue decomposition strategy to use. AMG requires pyamg
to be installed. It can be faster on very large, sparse problems.</p>
</dd>
<dt><strong>n_neighbors</strong><span class="classifier">int, default</span></dt><dd><p>Number of nearest neighbors for nearest_neighbors graph building.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int or None, optional (default=None)</span></dt><dd><p>The number of parallel jobs to run.
<code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <a class="reference external" href="https://joblib.readthedocs.io/en/latest/parallel.html#joblib.parallel_backend" title="(in joblib v0.14.1.dev0)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code></a> context.
<code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors. See <a class="reference internal" href="../../glossary.html#term-n-jobs"><span class="xref std std-term">Glossary</span></a>
for more details.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>embedding_</strong><span class="classifier">array, shape = (n_samples, n_components)</span></dt><dd><p>Spectral embedding of the training matrix.</p>
</dd>
<dt><strong>affinity_matrix_</strong><span class="classifier">array, shape = (n_samples, n_samples)</span></dt><dd><p>Affinity_matrix constructed from samples or precomputed.</p>
</dd>
<dt><strong>n_neighbors_</strong><span class="classifier">int</span></dt><dd><p>Number of nearest neighbors effectively used.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<ul class="simple">
<li><p>A Tutorial on Spectral Clustering, 2007
Ulrike von Luxburg
<a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.9323">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.9323</a></p></li>
<li><p>On Spectral Clustering: Analysis and an algorithm, 2001
Andrew Y. Ng, Michael I. Jordan, Yair Weiss
<a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.8100">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.8100</a></p></li>
<li><p>Normalized cuts and image segmentation, 2000
Jianbo Shi, Jitendra Malik
<a class="reference external" href="http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.2324">http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.2324</a></p></li>
</ul>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_digits</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.manifold</span> <span class="kn">import</span> <span class="n">SpectralEmbedding</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(1797, 64)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">embedding</span> <span class="o">=</span> <span class="n">SpectralEmbedding</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X_transformed</span> <span class="o">=</span> <span class="n">embedding</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X_transformed</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(100, 2)</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.manifold.SpectralEmbedding.fit" title="sklearn.manifold.SpectralEmbedding.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(self, X[, y])</p></td>
<td><p>Fit the model from data in X.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.manifold.SpectralEmbedding.fit_transform" title="sklearn.manifold.SpectralEmbedding.fit_transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code></a>(self, X[, y])</p></td>
<td><p>Fit the model from data in X and transform X.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.manifold.SpectralEmbedding.get_params" title="sklearn.manifold.SpectralEmbedding.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>(self[, deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.manifold.SpectralEmbedding.set_params" title="sklearn.manifold.SpectralEmbedding.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(self, \*\*params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.manifold.SpectralEmbedding.__init__">
<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">n_components=2</em>, <em class="sig-param">affinity='nearest_neighbors'</em>, <em class="sig-param">gamma=None</em>, <em class="sig-param">random_state=None</em>, <em class="sig-param">eigen_solver=None</em>, <em class="sig-param">n_neighbors=None</em>, <em class="sig-param">n_jobs=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_spectral_embedding.py#L448"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self.  See help(type(self)) for accurate signature.</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.SpectralEmbedding.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_spectral_embedding.py#L518"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model from data in X.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix}, shape (n_samples, n_features)</span></dt><dd><p>Training vector, where n_samples is the number of samples
and n_features is the number of features.</p>
<p>If affinity is “precomputed”
X : {array-like, sparse matrix}, shape (n_samples, n_samples),
Interpret X as precomputed adjacency graph computed from
samples.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Returns the instance itself.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.SpectralEmbedding.fit_transform">
<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_spectral_embedding.py#L559"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model from data in X and transform X.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix}, shape (n_samples, n_features)</span></dt><dd><p>Training vector, where n_samples is the number of samples
and n_features is the number of features.</p>
<p>If affinity is “precomputed”
X : {array-like, sparse matrix}, shape (n_samples, n_samples),
Interpret X as precomputed adjacency graph computed from
samples.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">array-like, shape (n_samples, n_components)</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.SpectralEmbedding.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L173"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">mapping of string to any</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.SpectralEmbedding.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.SpectralEmbedding.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<div class="section" id="examples-using-sklearn-manifold-spectralembedding">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.SpectralEmbedding</span></code><a class="headerlink" href="#examples-using-sklearn-manifold-spectralembedding" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="An illustration of various linkage option for agglomerative clustering on a 2D embedding of the..."><div class="figure align-default" id="id1">
<img alt="../../_images/sphx_glr_plot_digits_linkage_thumb.png" src="../../_images/sphx_glr_plot_digits_linkage_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cluster/plot_digits_linkage.html#sphx-glr-auto-examples-cluster-plot-digits-linkage-py"><span class="std std-ref">Various Agglomerative Clustering on a 2D embedding of digits</span></a></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="An illustration of dimensionality reduction on the S-curve dataset with various manifold learni..."><div class="figure align-default" id="id2">
<img alt="../../_images/sphx_glr_plot_compare_methods_thumb.png" src="../../_images/sphx_glr_plot_compare_methods_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/manifold/plot_compare_methods.html#sphx-glr-auto-examples-manifold-plot-compare-methods-py"><span class="std std-ref">Comparison of Manifold Learning methods</span></a></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="An application of the different manifold techniques on a spherical data-set. Here one can see t..."><div class="figure align-default" id="id3">
<img alt="../../_images/sphx_glr_plot_manifold_sphere_thumb.png" src="../../_images/sphx_glr_plot_manifold_sphere_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/manifold/plot_manifold_sphere.html#sphx-glr-auto-examples-manifold-plot-manifold-sphere-py"><span class="std std-ref">Manifold Learning methods on a severed sphere</span></a></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="An illustration of various embeddings on the digits dataset."><div class="figure align-default" id="id4">
<img alt="../../_images/sphx_glr_plot_lle_digits_thumb.png" src="../../_images/sphx_glr_plot_lle_digits_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/manifold/plot_lle_digits.html#sphx-glr-auto-examples-manifold-plot-lle-digits-py"><span class="std std-ref">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</span></a></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
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